I got a phone call saying I'm hired.

Interesting that they want you to work as a contractor for 90 days before bringing you on as an employee. One of the advantages to them in doing that is that they don't get dinged for any future unemployment benefits you receive if they end up not bringing you on as an employee. Future unemployment benefits would go back on the record of your previous employer and affect his unemployment insurance rates not the new boss's. Nice deal if he can pull it off. It also means that you won't be getting any other benefits that his employees get, such as insurance, accrued time off or sick time.

For your part it gives you the same 90 day period to determine if you want this job without affecting your rights to unemployment benefits from your old job. At least, that's the way it works in my state.

Depending on the state you live in you'll notify your unemployment office of your hours worked at your regularly scheduled update. In other words, if you work 40 hours next week then you'll put down 40 hours as contract labor when you file your weekly or bi-weekly update. You won't get compensation from the state for that week or any other week that you earn more than you would otherwise get through your unemployment. Don't close out your UE case though unless the state mandates it. You're being paid as a contractor and until you get employment then you'll still be able to file for weeks that you earn less than the benefit amount. There may be a limit to how long they'll let you do that.

As to negotiating the start time, I'd do it upfront (before the first day). If your work hours aren't going to be acceptable or mutually agreeable then you're better off knowing that upfront.

He didn't offer you a job. He offered you work. Working shouldn't eliminate your unemployment status, only the amount of the benefit received.